Problem: What do the following two equations represent? $-4x-2y = 1$ $12x+6y = 2$
Solution: Putting the first equation in $y = mx + b$ form gives: $-4x-2y = 1$ $-2y = 4x+1$ $y = -2x - \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $12x+6y = 2$ $6y = -12x+2$ $y = -2x + \dfrac{1}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.